add sqrt and cbrt (cubic roots finder) functions

README.md

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+# SICP

cbrt-test.rkt

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+#lang racket/base
+
+(require rackunit "cbrt.rkt")
+
+(check-equal? (round (cbrt 27)) 3.0 "Is cubic root of 27 is 3?")
+(check-equal? (round (cbrt 1000)) 10.0 "Is cubic root of 1000 is 10?")
+(check-equal? (round (cbrt 848471250563)) 9467.0 "Is square root of 848471250563 is 9467?")

cbrt.rkt

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+#lang racket
+
+(define (cbrt x)
+    (define (square n) (* n n))
+    (define (improve guess)
+        (/ (+ (* guess 2) (/ x (square guess))) 3))
+    (define (good-enough? previous-guess guess)
+        (< (abs (/ (- guess previous-guess) guess)) 0.00000000001))
+    (define (cbrt-iter guess)
+        (if (good-enough? guess (improve guess))
+            guess
+            (cbrt-iter (improve guess))))
+    (cbrt-iter 1.0))
+
+(provide cbrt)

sqrt-test.rkt

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+#lang racket/base
+
+(require rackunit "sqrt.rkt")
+
+(check-equal? (round (sqrt 81)) 9.0 "Is square root of 81 is 9?")
+(check-equal? (round (sqrt 4096)) 64.0 "Is square root of 4096 is 64?")
+(check-equal? (round (sqrt 9801)) 99.0 "Is square root of 9801 is 99?")

sqrt.rkt

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+#lang racket
+
+(define (sqrt x)
+    (define (square n) (* n n))
+    (define (good-enough? previous-guess guess)
+        (< (abs (/ (- guess previous-guess) guess)) 0.00000000001))
+    (define (average x y)
+        (/ (+ x y) 2))
+    (define (improve guess)
+        (average guess (/ x guess)))
+    (define (sqrt-iter guess)
+        (if (good-enough? guess (improve guess))
+            guess
+            (sqrt-iter (improve guess))))
+    (sqrt-iter 1.0))
+
+(provide sqrt)